To solve the problem of finding the smallest positive degree measure equivalent to [tex]\(\tan ^{-1}(3.27)\)[/tex], we can follow these steps:
1. Calculate the Angle in Radians:
The arctangent (inverse tangent) of 3.27 gives us an angle in radians:
[tex]\[
\theta_{\text{radians}} = \tan ^{-1}(3.27) \approx 1.274 \text{ radians}
\][/tex]
2. Convert the Radians to Degrees:
We need to convert the angle from radians to degrees using the conversion factor [tex]\(180^\circ/\pi\)[/tex]:
[tex]\[
\theta_{\text{degrees}} = 1.274 \times \frac{180}{\pi} \approx 72.996^\circ
\][/tex]
3. Find the Smallest Positive Degree Measure:
The angle we calculated in degrees is approximately 72.996 degrees. This angle is already within the range [0, 360) degrees, so there is no need for further adjustments.
Hence, the smallest positive degree measure equivalent to [tex]\(\tan ^{-1}(3.27)\)[/tex] is approximately 73 degrees.
Therefore, the correct answer is:
[tex]\[
\boxed{73^\circ}
\][/tex]
